A novel approach to estimated Boulingand-Minkowski fractal dimension from complex networks. (April 2022)

• Record Type: Journal Article
• Authors: de Sá, Luiz Alberto Pereira; Zielinski, Kallil M.C.; Rodrigues, Érick Oliveira; Backes, André R.; Florindo, João B.; Casanova, Dalcimar
• Is Part Of: Chaos, solitons and fractals. Volume 157(2022)
• Publication Date: 2022-04
• Subjects: Complex networks -- Fractal dimension -- Bouligand-Minkowski; 00-01 -- 99-00; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.111894
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Bouligand-Minkowski is based on the dilation of a shape with radius r. To use it on networks, edges are interpreted as pipes giving vent to some liquid. Vertices are end pipes and the dilation is the insertion of fluids in the system. Fluids are inserted into the edges by the vertex and shared with adjacent edges. Abstract: A complex network presents many topological features which characterize its behavior and dynamics. This characterization is an essential aspect of complex networks analysis and can be performed using several measures, including the fractal dimension. Originally the fractal dimension measures the complexity of an object in a Euclidean space, and the most common methods in the literature to estimate that dimension are box-counting, mass-radius, and Bouligand-Minkowski. However, networks are not Euclidean objects, so that these methods require some adaptation to measure the fractal dimension in this context. The literature presents some adaptations for methods like box-counting and mass-radius. However, there is no known adaptation developed for the Bouligand-Minkowski method. In this way, we propose an adaptation of the Bouligand-Minkowski to measure complex networks' fractal dimension. We compare our proposed method with others, and we also explore the application of the proposed method in a classification task of complex networks that confirmed its promising potential.